# Instructor Guide for Week 3

Week 3 is when the students get seriously into Matlab. The first lecture in this week is therefore devoted to the problem of relating declarative and imperative descriptions of signals and systems. This sets the framework for making the intellectual connection between the labs and the mathematics.

The rest of the week is devoted to introducing the notion of state and state machines. State machines are described by a function \set{update} that, given the current state and input, returns the new state and output. In anticipation of composing state machines, the concept of \textit{stuttering} is introduced. This is a slightly difficult concept to introduce at this time because it has no utility until you compose state machines. But introducing it now means that we don't have to change the rules later when we compose machines.

Note that the problem set this week has a significant Matlab component, and it is much easier for students to do it after they have done the lab. Thus, if you have Friday labs, you cannot have the homework due on Friday. It may be a good idea to have the homework due monday of next week even if the last lab is Thursday, to give students more time.

### Problem session

(For convenience, these problems have been collected).

- Brief introduction to Matlab, with a focus on everything being arrays, and the syntax for definining arrays. See the solution to lab 1.
- Chapter 1, problem 5 (Matlab) (Sampling a continuous-time signal and representing it in Matlab).
- Chapter 2, problems 2, 5, 11.